Terminal velocity

When something falls through a fluid (this can be a gas such as air or a liquid) it does not go on getting faster and faster. If it is falling through air the friction with the air slows it down. The maximum velocity that an object can reach in a given fluid is called its TERMINAL VELOCITY.

Remember that the greatest terminal velocity for a person falling through air near sea level is about 200 mph head down and about 125 mph lying flat out.






A certain person's terminal velocity will be different at different altitudes because of the different density of the air. The record free fall parachute jump at present was from around 30 000 m and the person fell over 10 000 m before opening their parachute. At these altitudes the terminal velocity is close to the speed of sound!

Falling through liquids

As we have said when objects fall through a liquid they get faster until they reach a speed called their terminal velocity. This is the fastest that they can fall in that liquid (usually a few cm/s). The actual speed is difficult to calculate except for spheres so we will just think about those.

This speed that objects reach depends on:
(a) the viscosity of the liquid. This is really how 'sticky' the liquid is. Syrup has a high viscosity while water has a low viscosity.
(b) the radius of the sphere – how big it is. Spheres with a large radius fall faster than ones of a small radius. It is the same with raindrops - big raindrops in a downpour fall really fast while small ones in drizzle just drift down.
(c) the density of the material of the sphere – steel spheres will fall faster than ones made of glass

When they are falling at their terminal velocity the drag on the sphere due to the viscosity of the liquid is equal to the weight of the sphere (minus any upthrust due to the liquid).